In a gas turbine, in each case a heat shield is arranged axially between two adjacent guide blades, this heat shield being fastened via a heat shield carrier to a stator or to the casing of the gas turbine. A corresponding construction also results for a rotor of the gas turbine, in which construction a heat shield may likewise be arranged between two adjacent rotor blades, this heat shield being fastened to the rotor by means of a heat shield carrier. The guide blades of the stator and the rotor blades of the rotor normally have a root which is designed as a blade carrier and with which the respective blade is anchored in the stator or the rotor. In this case, the blades of the gas turbine are arranged in a hot gas space of the gas turbine, hot gases flowing through this hot gas space during operation of the gas turbine. To cool the heat shield, a cooling space, to which a cooling gas is admitted or through which a cooling gas flows during operation of the gas turbine, is formed between the heat shield carrier and heat shield. A gap which is open toward the hot gas space and thus communicates with the latter is normally formed axially between a heat shield carrier and an adjacent blade carrier. In order to now prevent a gas exchange between the cooling space and the hot gas space, gap seals of the type mentioned at the beginning are used. For this purpose, a sealing body of the gap seal can be retained on the heat shield, on the one hand, and on the heat shield carrier, on the other hand, as a result of which effective sealing of the cooling space relative to the gap and thus relative to the hot gas space can be achieved.